Re: Suggestions for writing a Perl application

It's not at all impossible. Points can be on the line. If M and N are both odd, the line will go through at least one red and at least one blue point.

Of course, that still wouldn't address the problem with infinite sets.

In fact, it does work with infinite sets, and it works in more dimensions as well. This theorem, saying that in d dimensions, given d sets there is a hyperplane of dimension d - 1 that divides all sets in two parts of equal size, is also known as the "ham-cheese sandwich cut", because the theorem implies that you can always divide a ham-cheese sandwich in two equal parts (both parts having the same amount of ham, cheese and bread) with a single cut, even if you leave the cheese in the fridge.

Abigail

Comment on Re: Suggestions for writing a Perl application

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Re: Re: Suggestions for writing a Perl application by sauoq (Abbot) on Aug 29, 2003 at 23:06 UTC
Oh, duh. Points on the line. Right... my mistake. Regarding infinite sets, I simply meant that defining the problem in terms of `floor()` was problematic. You avoided that in your reply by using the phrases "two parts of equal size" and "two equal parts". -sauoq "My two cents aren't worth a dime.";	[reply]
Re: Suggestions for writing a Perl application by Abigail-II (Bishop) on Aug 29, 2003 at 23:43 UTC
Regarding infinite sets, I simply meant that defining the problem in terms of floor() was problematic. You avoided that in your reply by using the phrases "two parts of equal size" and "two equal parts". In my original statement of the problem, I was describing, finite, discrete sets. After all, I was saying one set had `N` points, the other `M` points. I would not be able to give a number of points if any of the sets was infinite. In my later reply, I was refering to the continuous form of the problem, in which we have continuous sets (but not necessarely connected). Then it's right to talk about two parts of equal size. Abigail	[reply]